Binary Image Reconstruction from Two Projections and Skeletal Information

  • Norbert Hantos
  • Péter Balázs
  • Kálmán Palágyi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7655)


In binary tomography, the goal is to reconstruct binary images from a small set of their projections. However, especially when only two projections are used, the task can be extremely underdetermined. In this paper, we show how to reduce ambiguity by using the morphological skeleton of the image as a priori. Three different variants of our method based on Simulated Annealing are tested using artificial binary images, and compared by reconstruction time and error.


Binary tomography Reconstruction Morphological skeleton Simulated annealing 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aert, S.V., Batenburg, K.J., Rossell, M.D., Erni, R., Tendeloo, G.V.: Three-dimensional atomic imaging of crystalline nanoparticles. Nature 470, 374–377 (2011)CrossRefGoogle Scholar
  2. 2.
    Batenburg, K.J., Bals, S., Sijbers, J., Kuebel, C., Midgley, P.A., Hernandez, J.C., Kaiser, U., Encina, E.R., Coronado, E.A., Tendeloo, G.V.: 3D imaging of nanomaterials by discrete tomography. Ultramicroscopy 109(6), 730–740 (2009)CrossRefGoogle Scholar
  3. 3.
    Baumann, J., Kiss, Z., Krimmel, S., Kuba, A., Nagy, A., Rodek, L., Schillinger, B., Stephan, J.: Discrete tomography methods for nondestructive testing. In: Herman, G.T., Kuba, A. (eds.) Advances in Discrete Tomography and Its Applications, pp. 303–331. Birkhäuser, Basel (2007)CrossRefGoogle Scholar
  4. 4.
    Di Gesù, V., Lo Bosco, G., Millonzi, F., Valenti, C.: A Memetic Algorithm for Binary Image Reconstruction. In: Brimkov, V.E., Barneva, R.P., Hauptman, H.A. (eds.) IWCIA 2008. LNCS, vol. 4958, pp. 384–395. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Giblin, P., Kimia, B.B.: A formal classification of 3D medial axis points and their local geometry. IEEE Trans. Pattern Analysis and Machine Intelligence 26(2), 238–251 (2004)CrossRefGoogle Scholar
  6. 6.
    Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 3rd edn. Prentice Hall (2008)Google Scholar
  7. 7.
    Herman, G.T., Kuba, A. (eds.): Advances in Discrete Tomography and Its Applications. Birkhäuser, Boston (2007)zbMATHGoogle Scholar
  8. 8.
    Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P.: Optimization by Simulated Annealing. Science 220, 671–680 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Nagy, A., Kuba, A.: Parameter settings for reconstructing binary matrices from fan-beam projections. Journal of Computing and Information Technology 14(2), 100–110 (2006)CrossRefGoogle Scholar
  10. 10.
    Ryser, H.J.: Combinatorial properties of matrices of zeros and ones. Canad. J. Math. 9, 371–377 (1957)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Schüle, T., Schnörr, C., Weber, S., Hornegger, J.: Discrete tomography by convexconcave regularization and D.C. programming. Discrete Applied Mathematics 151, 229–243 (2005)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Norbert Hantos
    • 1
  • Péter Balázs
    • 1
  • Kálmán Palágyi
    • 1
  1. 1.Department of Image Processing and Computer GraphicsUniversity of SzegedSzegedHungary

Personalised recommendations